Question

The window shown in the shape of a semi-circle with radius 4 ft. The distance from S to T is 2 ft and the measure of $\widehat{AB}={45}^{\circ }$. Area of glass in the region ABCD is

• A. 4.7 sq ft
• B. 4.9 sq ft
• C. 4.5 sq ft
• D. 5 sq ft

Answer 1

The correct option is A 4.7 sq ft

Given $r_1=4$ and $r_2=2$

Required area = Area of sector OAB - Area of sector ODC
$=\pi r_1^2\times \frac{\theta }{{360}^{\circ }}-\pi r_2^2\times \frac{\theta }{{360}^{\circ }}$
$=\pi r_1^2\times \frac{{45}^{\circ }}{{360}^{\circ }}-\pi r_2^2\times \frac{{45}^{\circ }}{{360}^{\circ }}$
Taking common terms and solving we get,
$=\frac{\pi }{8}(4^2-2^2)=\frac{\pi }{8}\times 12=4.7sq.ft$